The teacher asks the students to consider reasons why some coins do not have mint marks. Then he pushes them to think about which mints can likely be eliminated based on the information they see across the four line plots.

b.

Some students think the coins with no mint marks were just mistakes. Others think that those coins are likely to be from Philadelphia, because so many nickels contain the Philadelphia mint mark. When thinking about which coins could be eliminated, the students eliminate Denver first and then San Francisco.

c.

At first, students are reasoning more from their own personal judgement, such as when one student says that the missing mint marks are a mistake because the machines were working too fast. Other students' comments were more grounded in the data.

One example of a conjecture that students might make is "Philadelphia produces more nickels than the other mints." This could be formulated as a new question to be investigated: "Does Philadelphia produce more nickels than the other mints?" The students could investigate this question in several ways. They might want to just enlarge their own sample of nickels, with each student collecting nickels over the next week for further analysis. This could also evolve into an Internet project in which your students contact students in other parts of the country, especially those who live closer to the other mints. Each group of students could collect and analyze a sample of nickels. They could then compare across samples and finally combine them into one larger sample.